Effects of polydispersity on hard sphere crystals

Abstract

We use simple models and molecular dynamics simulations to determine the effects of polydispersity δ on the equation of state for hard sphere crystals. Experiments show that the osmotic pressure for poly-(methyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic acid) (PHSA) layer with a 5% polydispersity exceeds the value expected for hard spheres as the volume fraction φ increases, particularly for φ>0.60. Mean field theory predicts a higher osmotic pressure with increasing polydispersity, but the effects are only significant for δ>0.10. Molecular dynamics simulations with δ=0.05 bound the equation of state between a metastable disordered upper limit and a crystalline organized polydisperse (possibly) lower limit. The pressure for the PMMA-PHSA spheres lies close to the organized polydisperse limit, indicating a preference for a crystalline ordered arrangement where smaller particles surround larger ones. Thus, the higher osmotic pressure seen in the equation of state of PMMA-PHSA spheres is a direct effect of polydispersity, manifest as a pronounced reduction in the crystalline close packed volume fraction from φmax(FCC, δ=0)=0.7404 to φmax(FCC, δ=0.1)=0.665. The random close packing φmax(RCP) is almost independent of polydispersity. This leads to a crossing of values of φmax(FCC) and φmax(RCP) and hence a possible terminal polydispersity of 0.12±0.01, consistent with other simulations, theories, and experiments. Since our results do not include size fractionation of the liquid and solid, the exact meaning of this crossing is unclear and its agreement with previously reported terminal polydispersities may be coincidental.

Equilibrium Phase Behavior of Polydisperse Hard Spheres

“…[6] has a more detailed bibliography of earlier work. These studies have revealed that, compared to the monodisperse case, polydispersity causes several qualitatively new phenomena.…”

“…The effect of polydispersity on the phase behavior of hard spheres has been investigated by experiments [1, 2], computer simulations [3,4,5,6], density functional theories [7,8], and simplified analytical theories [6,9,10,11,12,13,14]; Ref.…”

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…The formation of a hybrid colloidal film consisting of a mixture of an equal number of two PS spheres (d=300 nm and d=360 nm) artificially broadens the size distribution beyond the polydispersity limit of about 5% necessary for crystallization. [152] Indeed, the crystallization is prohibited in this hybrid colloidal film, as indicated by the lack of a long-range order in the right-hand panel of parently, the crystalline order is a prerequisite for the BG but not for the newly observed lower frequency HG, which is omnidirectional in the colloidal glass. An identification of the latter as a theoretically anticipated HG, [153] through density-of-states (DOS) calculations, [80] is examined in Fig.…”

“…5.6). Since the size difference is clearly below 5%, [152] the particles form random co-crystals during vertical lifting deposition under stirring. Fig.…”

Spinodal instabilities in polydisperse lyotropic nematics

“…One of the main complications of these systems is that their multi-component character enables coexistence of arbitrarily many fluid or solid phases each accommodating a specific subpopulation of the overall distribution. A prominent example are dense fluids of polydisperse spherical particles where the presence of a range of different sizes may lead to a suppression of crystallization [42,43] in favour of various amorphous states whose nature has been the subject of recent simulation studies [44][45][46]. Alternatively, size polydisperse sphere fluids may develop a coexistence of a number of different solid phases following a pathway referred to as fractionated crystallization [47].…”